GCSE Mathematics (Higher)

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Revision Booklet 2

Questions

Q1. 

The population of a city increased by 5.2% for the year 2014

At the beginning of 2015 the population of the city was 1560 000

Lin assumes that the population will continue to increase at a constant rate of 5.2% each year.

(a)  Use Lin's assumption to estimate the population of the city at the beginning of 2017       Give your answer correct to 3 significant figures.

...........................................................

(3)(b)  (i)  Use Lin's assumption to work out the year in which the population of the city will             reach 2 000 000

...........................................................

(ii)  If Lin's assumption about the rate of increase of the population is too low,       how might this affect your answer to (b)(i)?

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(3) 

(Total for question = 6 marks)

Q2.

Derek buys a house for £150 000 He sells the house for £154 500

(a) Work out Derek's percentage profit.

 

 

 

 

 

 

      ..............................................................................................................................................(3)

Derek invests £154 500 for 2 years at 4% per year compound interest.

(b) Work out the value of the investment at the end of 2 years.

 

 

 

 

 

 

      ..............................................................................................................................................(3)

(Total for Question is 6 marks)

Q3. 

Three companies sell the same type of furniture.

The price of the furniture from Pooles of London is £1480 The price of the furniture from Jardins of Paris is €1980 The price of the furniture from Outways of New York is $2250

The exchange rates are

£1 = €1.34£1 = $1.52

Which company sells this furniture at the lowest price? You must show how you get your answer.

 

(Total for question is 3 marks)

Q4. 

−5 < y ≤ 0

y is an integer.

(a) Write down all the possible values of y.

...........................................................(2)

(b) Solve 6(x − 2) > 15

...........................................................(2)

(Total for Question is 4 marks)

Q5. 

Here is a spinner. When the arrow is spun once, a 1 or a 2 or a 3 can be scored.

Bill is going to spin the arrow twice. He will work out his total score by adding the two scores he gets on the two spins.

The probability that he will get a total score of 4 is

Assuming that the thickness of the three lines between the sectors may be ignored,

Work out the value of x.

 

(Total for question = 5 marks)

Q6.

 

The diagrams show a sequence of patterns made from grey tiles and white tiles.

The number of grey tiles in each pattern forms an arithmetic sequence.

(a)  Find an expression, in terms of n, for the number of grey tiles in Pattern n.

(2)

The total number of grey tiles and white tiles in each pattern is always the sum of the squares of two consecutive whole numbers.

(b)  Find an expression, in terms of n, for the total number of grey tiles and white tiles in Pattern n. Give your answer in its simplest form.

(3)

(c)  Is there a pattern for which the total number of grey tiles and white tiles is 231? Give a reason for your answer.

(2)

The total number of grey tiles and white tiles in any pattern of this sequence is always an odd number.

(d)  Explain why.

(2)

 

(Total for question = 9 marks)

Q7. 

(a)  On the grid, construct the graph of x2 + y2 = 16

(2)

(b)  Find estimates for the solutions of the simultaneous equations

x2 + y2 = 16            y = 2x + 1

...........................................................

(3) 

(Total for question = 5 marks)

Q8. 

The diagram shows a regular octagon and a regular hexagon.

Find the size of the angle marked xYou must show all your working.

x =........................................................... º

 

(Total for question = 3 marks)

Q9. 

ABCDE and PQRST are regular pentagons.

SR is parallel to DCAP = BQ = CR = DS = ET

Work out the size of angle SRC. You must show all your working.

........................................................... °

 

(Total for question = 3 marks) 

Q10. 

VABCD is a solid pyramid.

ABCD is a square of side 20 cm.

The angle between any sloping edge and the plane ABCD is 55°

Calculate the surface area of the pyramid. Give your answer correct to 2 significant figures.

...........................................................cm2

 

(Total for question = 5 marks)

Q11.

* There are two trays of plants in a greenhouse. The first tray of plants was given fertiliser. The second tray of plants was not given fertiliser.

On Monday the heights of the plants were measured in centimetres.The boxes show some information about the heights of the plants.

Compare the distribution of the heights of the plants given fertiliser to the distribution of the heights of the plants not given fertiliser.

 

 

 

 

 

 

 

 

 

(Total for Question is 4 marks)

Q12.

Jim went on a fishing holiday. The histogram shows some information about the weights of the fish he caught.

(a) Use the histogram to complete the frequency table.

(2)Jim kept all the fish he caught with a weight greater than 2000 g.

(b) Find the ratio of the number of fish Jim kept to the total number of fish he caught.

      ..............................................................................................................................................(2)

(c) Use the histogram to find an estimate of the median.

 

      ..............................................................................................................................................(2)

(Total for Question is 6 marks)